Uses of a small field value which falls from a metastable maximum over cosmological times


We consider a small, metastable maximum vacuum expectation value b0b_0 of order of a few eV, for a pseudoscalar Goldstone-like field, which is related to the scalar inflaton field ϕ\phi in an idealized model of a cosmological, spontaneously-broken chiral symmetry. The b field allows for relating semi-quantitatively three distinct quantities in a cosmological context. (1) A very small, residual vacuum energy density or effective cosmological constant of ~ lambda b_0^4 ~ 2.7 x 10^{-47}GeV^4, for lambda ~ 3 x 10^{-14}, the same as an empirical inflaton self-coupling. (2) A tiny neutrino mass, less then b_0. (3) A possible small variation downward of the proton to electron mass ratio over cosmological time. The latter arises from the motion downward of the bb field over cosmological time, toward a nonzero limiting value as tt \to \infty. Such behavior is consistent with an equation of motion. We argue that hypothetical b quanta, potentially inducing new long-range forces, are absent, because of negative, effective squared mass in an equation of motion for bb-field fluctuations.Comment: version accepted for publication in Mod.Phys.Lett.

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